发表机构
Fermi National Accelerator Laboratory; European Organization for Nuclear Research (CERN)（费米国家加速器实验室; 欧洲核子研究组织（CERN））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究近似量子纠错中优化问题，利用恢复与环境解耦对偶性及噪声克劳斯算子衰减权重，建立降维框架，实现计算加速，为AQEC码高精度优化提供可能。
AI 中文摘要
近似量子纠错（AQEC）不仅决定离散和连续变量量子纠错码的性能，还作为跨物理学科的统一框架。通过标准半定规划识别最优恢复信道以最大化纠缠保真度，因克劳斯算子数量随系统规模指数增长而存在计算瓶颈。虽有解析近最优映射，但通常仅在近满足基尔 - 拉弗拉梅条件时有效。本文利用恢复与环境解耦的对偶性建立有效框架，得到比转置信道设定的传统极限更紧的纠缠保真度解析下界。通过利用噪声克劳斯算子的衰减权重，引入基于主成分分析的框架降维。在热损耗信道中权重指数衰减时，该方法实现33倍计算加速且保持严格精度，使先前因维度诅咒难处理的AQEC码高精度优化成为可能。
英文摘要
Approximate quantum error correction (AQEC) extends the framework of discrete- and continuous-variable quantum error correction beyond the Knill-Laflamme (KL) conditions, where the recovery performance is quantified by entanglement fidelity. Recent studies have enabled efficient evaluation of near-optimal entanglement fidelity using transpose-channel recovery. Yet, determining the global optimal recovery map and its entanglement fidelity for general codes beyond the KL conditions remains a major computational challenge. Direct optimization becomes prohibitive as the number of noise Kraus operators grows rapidly with system size, and existing approaches lack rigorous guarantees for reducing this optimization to a tractable dimension. Here, we derive an explicit characterization of the optimal environmental state of complement channel, which transforms the optimization over recovery channels into an equivalent optimization over quotient unitaries. For a broader class of codes that satisfy only the orthogonality part of the KL conditions, we show that the optimal recovery map admits an explicit analytical form. Building on this form, we derive novel rigorous lower bounds of entanglement fidelity that strictly improve upon the transpose-recovery bound. We further develop a novel recovery strategy based on principle components, and derive a rigorous bound on the error introduced by noise truncation. Our approach enables efficient searches for approximate recovery maps for AQEC codes, avoiding the need to optimize over the full Kraus-operator space.
